Have been building a 600-based Abarth replica and restoring a Abarth 1300/124 (850-based). Have been into these rear-engine Fiats a very long time. Some [rambling] thoughts...
I would say there are a lot more standard and performance parts still available for 600 sedans simply due to the fact that they made millions of them over the years plus that they were
very popular in racing in Europe back in the day. Owners raced them and also upgraded them for street use around the world. Abarth added to their popularity by offering performance exhausts in the beginning and then more and more street and race parts as time went by. You can still find a wide range of performance parts for them, many of which are replica Abarth parts from vendors such as Berni Motori in Italy. Check out their online catalogue. Original used Abarth parts, when and IF you can find them these days, usually have instant nose bleed prices. Replica prices aren't exactly cheap either. I collected a lot of 600 performance parts off ebay around a dozen years ago when ebay was in it's heyday for vintage parts and got many at reasonable prices and many 600 performance parts were available. When Scuderia Topolino was still in the US, Paul V. had a huge range of 600 & 850 performance parts, mostly 600 stuff. When he sold the company and it moved to Germany, many parts are no longer offered but there are still some good parts. Some good parts can still be found on ebay Italy but some have crazy high mafia-inspired prices. The 600 sedans eventually became highly developed race cars in Europe and in the US. The later Berlina Corsa models were so fast and winning so many races in the US that the SCCA ended up banning them.
Then there was Al Cosentino and Faza that was a big factor in the popularity in the US of 600s and 850s for both racing parts and street performance parts. According to Al, the latest iteration of a Berlina Corsa model he owned had fuel injection that produced 125 HP out of a 1 liter engine. That is ridiculously high HP per liter for any nat. aspirated engine. When I was in college in the 70s I used to sit at the back with the Faza "Bible" propped up behind a notebook drooling away. Ah, the ol' pre-internet days...
The 600 chassis and other parts also became the foundation for numerous derivatives like the Abarth Zagato-bodied Double Bubble & Record Monza, Allemano coupe & spider, Cisitalia and Abarth record cars. The 600s were also manufactured in other countries under different names - Zastava and Seat. Not sure about Seat but Zastava was produced much longer after Fiat stopped production. This makes finding some parts easier as well as cheaper. A Zasatava dual master brake cylinder is a recommended upgrade for a 600 performance car.
For 600s, you can still get things like sway bars, lowered springs, coil-over front springs/shocks, fender flares & front radiator shroud (in late and early styles), Abarth oil pans, raised engine lid props, CV jointed axles, etc. and many engine parts. Some engine parts are interchangeable with 850 series engines but you need to know what you're doing. IMO, stock parts for 600s are more available compared to 850s, especially the coupes which had relatively low production numbers. Some 850 parts like brake calipers can be used in 600s.
Yes, rotation is different between 600 & 850 engines. A popular performance upgrade in 600s is to just drop in an Abarth Autobianchi A112 1050cc engine which is the same rotation as a 600 and has 70 HP in stock form. In the beginning, the early 633cc 600 engine only put out less than 25 HP. The 850 series engines can be reversed with the correct parts and a few mods. A 903 cc engine is a good choice for a more power. The 850 engines are tilted slightly compared to 600s and while oil pans and intake manifolds are interchangeable, they won't sit level. The 850 engines are basically a progression of the 600 engines and both had various revisions over the years. Abarth even used the 124 OHV engine in the 850-based 1300/124 and derivatives like the Scorpione. The special bellhousing adapter is still available at Berni Motori. There was also a "radiale" version of the engine with hemispherical combustion chambers for both the 600 and 850s. There are lots of performance parts still around for 850 engines and can end up with a lot more HP than compared to a 600 engine.
I have a 1050cc performance motor for my 600 built on a 903 block. It has A112 pistons, rods, crank, cam & head; Weber DCD carb; a few trick parts like titanium valve springs retainers; PBS water pump; rotating parts balanced; some porting on head. I collected most parts off ebay and Paul. V. did the machining and assembly work (just before he retired). I wanted the engine to look more like an original 600 one and not an obvious A112 one. Will put out up to 90 HP.
There was the early 600 model with suicide doors, 633cc engine and parking brake drum on the front of the transaxle. The later 600D models had 747cc engines, normal-opening doors and parking brakes on the drums at the wheels. For advanced performance driving (ie., more aggressive) you want the later 600D transaxle since it is stronger. There isn't otherwise much difference between early and late models. Note that 600/600D transaxles have a non-synchro 1st gear and any 600 you buy is likely to have damaged teeth as well as worn synchro rings.
Nowadays you will rarely find a genuine 600 Abarth with it's original engine due to the ultra-rarity of parts as well as cost. Most will have an 850-based motor or sometimes the A112 motor, depending on race regs. Below is a later Berlina Corsa engine with remote oil cooler where the rad normally is, oil catch tank, coolant expansion tank on right wall and the strengthening piece on the engine mount panel. Super sexy and kinda takes your breath away!! What Abarth did to these engines is truly amazing. Engine is not original Abarth and is an A112 unit, identifiable by the block-mounted oil filter. Some Abarth Record Monza cars had an overhead chain-driven twin cam engine based on a 600 block.
The 600s and 850s have quite different "characters". Bone stock 600s are more like an old lady's car and not all that appealing to most buyers unless you wanted one for a collection or maybe for sentimental reasons. Most buyers likely want to do some sort of performance upgrade. A bone stock 850 spider or coupe is way more desirable in comparison. I think you could say an 850 sedan isn't exactly a head-turner. The Abarth Berlina Corsa below is a later model with whale-tail fiberglass engine lid, wide rear fenders and raised & widened front fenders. The all white 600 below is a '62 850 TC model with various exterior items that identify it as a true Abarth - front trunk lid "swallow", grille & whiskers, Fergat wheels, emblems on fenders and very early style front rad. All these can easily be added to a stock 600 to make a faux Abarth.
You could take a 600 and do a lot of performance upgrades without trying to make it look like an Abarth and have a car that is a lot of fun to drive. Trying to make it look like an Abarth can add a lot of cost and work.
There are many performance and upgrade parts available for 850s and many things you can do to improve performance. A few parts are impossible or hard to find such as a heavier rear sway bar and shocks like Koni. Lots of 850 spiders were used in racing in the US and some coupes. I still remember an 850 coupe from Seattle that came up to our local track (Westwood) back in the 70s. I just loved the looks and the fact that it was modified for racing.
The wheelbase of a 600 is a bit less and they are a bit lighter. An 850 and 600 have a similar front suspension and rear trailing arm setup. I don't think there's a big difference in how they handle and drive and it will depend a lot more on how you modify the suspension, improve braking, increase HP, etc. IMHO, the 600 will be more unique when done up. And fun when you pull up beside a hot car at a stoplight and leave it in the dust, lol.
If you do decide to go for a 600, you may be interested in a few parts I have available for sale like Abarth large style rear fenders and front rad shroud, trailing arms with brackets for disc brakes, 600D transaxle and various used parts I've gathered over the years. Finding a parts manual with part numbers would really help. (I think I have an extra.) If you look at a 600 for sale, look very closely at all the body seams as they are moisture traps that can cause serious rust, some of which may not be readily visible. Fiat did not use any rust protection on these cars.
Choose wisely and have fun!