Well, relying on presets only wil limit you with any synth no matter how flexible and wonderful it's tone architecture and capabilities are. I don't recommend that approach to anyone who knows and expects certain kind of sounds out of their instruments. Knowing what you want is good but there is no majic device out there to do it all for you. Since you are well setup to run soft synths I suggest you mess with that option.

My favorite drum synth is waldorf Attack. It is available both as a rack and a VSTi. Waldorf are out of business so finding the rack module will be a bit tricky. However the VSTi version (that doesn't lack in anything when compared to the rack) is still sold by Steinberg who originally distributed it anyway.

Atttack is basically a very complex synth that is mostly based on analog modeling (has a couple of sampled crashes but that's it. The rest is generated by it's synth engine) with very flexible tone architecture generally needed to produce sound FX and drum sounds. The sounds that you seem to be after (at least according to your description) are most likely a result of a combination of analog drum sound modules, mono/poly analog synths and some DSP FX (like Delay, Flange, Chorus(.
Attack is all of the above. Designed specifically for percussion and sound FX. It is also possible to use it for sweeps, basses, leads etc. But it's strength is in making drums and FX.

Synthetically speaking it features an oscillator (that can generate anything from White noise to Square and saw waveforms(, very flexible modulation matrix, multiple filter types with pretty real sounding resonance and optional self oscillation, easy to control snappy Envelopes and LFOs and some DSp FX as well (some dsp like Delay and Flange is done per drum sound). So it is a little monster. Very easy to program.
While it's presets cover mostly techno-electro-house type sounds it is well capable of heavy electronic reggae sounds and sound FX.

Battery on the other hand is mostly a sample playback module so really, it isn't anywhere near as flexible as a synth. I prefer NI FM7 for drums. Of coarse this means FM programming which I dont' recommend you get into yet.

Start with Attack. Download a demo or something. If there are only audio demos then there is no crime in downloading a kracked version just to try it. As long as you don't use it for any commercial purposes you're not breaking any laws. Once you've familiarised yourself with it's tone architecture and tried it to see if it can do what you like you'll buy one.

Also, take some time to read up on synthesis and try to familiarise yourself with different types of synthesis. It always helps to know the difference between samples, FM, analog, additive, granular, wavetable and other forms of synthesis. Otherwise you can get very very very confused very quickly.

I'm pretty sure Reason is well capable of playing drum samples that you like. Of coarse without you knowing how to add your own samples into it's library (and where to get those samples as well as what to look for( it isn't going to be useful to you.

Part of using synths is knowing them. we all had to start somewhere and without that knowledge you will pretty much continue wondering around in the dark and getting nowhere.

-ED-