Among other macros, I have and use the Canon EF 100/2.8... and I don't plan to "upgrade" to the 100L IS.
For one thing, stabilization is of limited use at macro magnifications. The 100L IS uses a hybrid form of stabilization that's probably the best system on any macro lens, but it's only good for roughly 1 stop or less of assistance at 1:1 magnification. Most other macro lenses with some form of stabilization (Nikon 105 VR; Tamron 90 VC; Sigma 105 OS, 150 OS and 180 OS) give virtually no assistance at 1:1, and only a little at 1:2.
The stabilization is more likely to be helpful if using the lens at non-macro distances, such as for portraits. But for macro work I'd rather put my money into a tripod mounting ring, than spend it just to get stabilization.
However, personally I also don't particularly like macro lenses for portraits. They are simply too sharp and don't enjoy large enough aperture for extremely shallow depth of field/strong background blur effects. Instead of my 100/2.8 macro, I use 85/1.8 or 135/2 for portraits, which have 1.33 and 1 stop advantages, respectively. Stopped down a little, both of those lenses are plenty sharp for portraits, without being ridiculously so. Wide open, they both have ability to strongly blur down a background... the 135mm in particular.
Image quality and build quality of the two Canon 100mm are virtually the same. Both can be fitted with tripod mounting rings (a BIG selling point IMO). Both are internal focusing (IF) lenses, same as your EF-S 60mm, so they don't grow larger when focused closer (but start out larger and actually change their "true" focal length a little during focusing).
The 100L IS costs $950 and comes with a matching lens hood, but not the tripod ring. That's sold separately... $172 for the Canon OEM Tripod Ring D.
The 100/2.8 USM costs $600, but doesn't include the matching hood... it's another $36 for that. The Tripod Ring B for it costs $140.
The 100L IS might have slightly better background blur, thanks to a 9-blade aperture. The 100/2.8 USM uses an 8-blade aperture. AFAIK neither lens uses curved aperture blades.
The 100L IS uses 67mm filters, while the 100/2.8 USM uses 58mm.
The 100L IS has a three-range focus limiter, while the 100/2.8 USM has a two-range limiter. Both have USM, which is reasonably fast, but not as instantaneous as non-macro USM lenses around the same focal length. I wouldn't use either for sports shooting, for example.
Besides the EF 100/2.8 USM (with tripod ring & hood), other macro lenses I use personally are: Tamron SP 60/2.0(crop only), Canon MP-E 65mm, Tamron SP 90mm f2.8 (vintage/manual focus), and Canon EF 180/3.5L USM. I also frequently use Canon TS-E 45mm and Canon EF 300/4L IS USM for near macro/close-up work.