Things you can upgrade/repair beside caps:
- Bridge rectifier
- Switching transistors on the primary side
- Rectifier diodes on the output, especially if the original ones are undersized
- Fan, if you want a more silent one or the current one breaks
You can also upgrade the capacitors on the input line filter with safety rated caps if the PSU uses generic caps there.
What is usually very difficult to replace is custom made parts like transformers, so unless you take one from another identical PSU I wouldn't suggest trying to mess with those. But transformers don't fail very often unless there's some sort of catastrophe. Inductors/coils are also typically difficult to replace if you don't know the values, you can use an inductance meter but I don't think they're precise enough.
What I take into account when deciding whether I should attempt to repair a PSU is:
- Is it at least of decent quality? You can't really fix things like poor design (no OCP/OVP, wimpy heatsinks, and so on) so I don't bother with those
- Was there any catastrophic failure? If there are holes in the PCB or some major damage I wouldn't risk trying to fix it
In general I recommend refurbishing older power supplies of good quality instead of buying new >700W monsters to use in retro PCs. The learning curve is not very steep, if you have basic soldering experience it will be very easy to work with single sided PCBs.
Also, I find many inconveniences to buying modern high-power units such as: price (not just the PSU but also the SATA->Molex/Floppy and ATX->AT adapters you need to buy), high current output that could cause trouble in the case of a short, bottom fan placed upwards ends up being blocked by the top of a baby AT case, and finally I personally feel they look completely out of place in an older case.