1 amp is high current?

I'm assuming they mean high-current relative to the TTL and CMOS current levels. A 1-Amp H-Bridge is definitely not what you'd be using in your BattleBot but it's a common power range for small robots. The Dallas Personal Robotics Group H-Bridge Board is also in the 1-Amp range (with a 3-amp peak, I believe), as are several other common H-Bridge kits.

Like an h-bridge over troubled water, I will look down and say Hi current...

I guess that's how hi current is different than high current. I looked at the picture of it: it's a dip chip on a carrier board with no heat sinks. Because of that I'm guessing 1 amp is really really pushing it. I'd thank at $20 it would be a great board for a modest little robot that has less than 2" diameter gearhead motors. Probably wouldn't want to stall the motors, and probably want to add some glue- on type heat sink or also a little fan for more cooling. It's kinda marginal, but for $20 though, it looks quite tempting.

That's just my guess. [insert disclaimer here]

The DPRG board uses an L298 chip which I believe will do 1amp constant and 3amp peak. The New Micros board looks like one of those LMD293D chips which will do like 300ma constant and 1amp peak. So when they say it'll do 1 amp, that's really a stretch. I'm guessing this chip on the New Micro's board is very similar to an 293 chip since it's a DIP with no place for a heatsink whereas an L298 has a big old ground plate with a place for a large heatsink. I'd much rather have the DPRG board, even if I did lay it out. :-)

The New Micros h-bridge uses the TI 754410, pin compatible with the L293D. The 754410 can sort of carry an Amp continuous, 2 A peak, and New Micros had a cool little IC sink I saw on the ones they had at the shop. Package dissipation is 2075 mW continuous, though. One thing that really helps is a good size ground plane on the PCB to help dissipate the heat. That with the IC heat sink and thermal protection circuitry on the 754410 should make it pretty tough. I've used these on a robot that had 2 motors that stall a bit over an Amp each, with no smoked 754410 yet. Clay T smoked one on a robot of his, and Chuck McM did as well, but ya just shouldn't try to run big motors with these. TI datasheet here.

We did a thorough test of the 754410 versus the venerable L293D. We got a marginal amount of additional power from the 754410 (practically neglible), but also discovered that the L293D has the surprising benefit of having input logic levels of Gnd to Vcc - of the supply power!

Yup, you can run logic "high" as high as your chip supply, being as high as 36 volts. If you're really into a tight spot with no way of accessing TTL/CMOS logic levels, screw'em! Use the Vcc of the motor supply line!

Of course, the 754410 has standard inputs, so going too high on the inputs will toast it.

For the difference in price and availability, a properly heat- sinked L293d is practically as good as the 754410.

Funny for all the advances in electronics, motor drivers have fallen back to being uC controlled FETS for the most part. Check a hard-drive PCB when you get the chance - it most likely will have 4 easily identifiable FETS, not an all-in-one IC. It's either that, or one of the newer SMT-style Allegro (or similar) devices that aren't available in DIP packaging...