If you're comparing a diesel 80-series to a Surf, then you'll be looking at the 1HZ, 1HD-T (or -FT/FTE) to a 2L-TE or 1KZ-TE.
Pros of the 80-series platform will be a much more robust build, bigger vehicle (more interior space, better leg room and driving position), solid front axle, full-time 4wd, bigger, more powerful engine options (4.2L inline 6-cylinder, NA or turbo) and overall a more comfortable vehicle with more options. JDM models came with options like triple locking differentials, factory winch, heated seats, climate control, refrigerated center console, and more.
Cons of the 80-series are: hard to find in manual transmission variants, lower fuel economy (expect mid teens to possibly low 20's mpg), not cheap to maintain ($30+ oil filters, 12qt oil capacity, for example), larger exterior dimensions can be tricky on tight trails.
Pros of the Surf: small and nimble, better fuel economy (low to mid 20's mpg), more likely to be available with a manual transmission, somewhat cheaper to maintain (still not a cheap as something US-spec), more basic and simple overall.
Cons of the Surf: engines aren't as reliable (2L-TE can overheat easily and crack cylinder head, 1KZ-TE less so but still possible), lower powered (2L-TE will be slow, 1KZ-TE shouldn't be too bad), electronic engine management systems are old and often require maintenance, not as robustly built as the 80-series, IFS, fewer options and creature comforts, small inside with somewhat cramped driving position.
Aftermarket support for both platforms is quite good, since both were sold in the US with different engines. The Surf will require more upgrades and involved ownership to keep it running well and prevent the common engine failures, but will be cheaper to purchase and run on a daily basis than an 80. It really boils down to the kind of driving and ownership experience you want. Given equal, stock condition at purchase, a Surf will be more of a project than an 80. I've had both an HDJ81 and an LN106 Hilux (basically the trimmed down, no-frills pickup version of the Surf) and have a friend who had a Surf. The 80-series feels much more composed both on and off road, and is a tank-like driving experience with plenty of power for modern traffic. The Surf is small and light, feels more cheaply built and basic. The 2L-TE version is a little on the slow side for modern traffic, but a 1KZ-TE powered example should do just fine.