REL Vs SVS for 2 channel music listening

I don't think the subwoofer is the issue, but rather the interaction with the room. Just look at some REW waterfall plots. Subwoofers produce low frequencies and hence room modes. To cure this you need a larger room (because in a large room room modes occur at lower and hence less obnoxious frequencies), use multiple subs (two are often enough) to even out the response over a larger area, and use dsp room equalization such as the DSPeaker Antimode 8033.
At your budget I would get two SVS SB1000 subs plus an Antimode 8033. If your room is large I would save up for two SB2000 subs.
For some reading material, see here: http://www.acousticfrontiers.com/20101029using-multiple-subwoofers-to-improve-bass-the-welti-devanti...

Rel makes fine subwoofers, no doubt. They also look good, but are relatively expensive.
For a while their unique selling point was that they connected at speaker level, and without a high pass filter for the main speakers. Hence their typical low pass crossover point had to be and was relatively low, with as little impact on the main speakers as possible.. These days, many other subs can do the same.
To be honest the sound quality of a sub is largely determined by the room. 'Speed' for example is an acoustic property and not as some seem to think a driver issue. Just look at REW waterfall graphs. Room modes are a nasty problem, only really solved by the combination of multiple subs and room eq.

Don't forget to treat yourself to an Antimode 8033 room eq as well.

Assuming this is about an Antimode 8033. It will only equalize automatically. You insert it in the signal chain, plug in the supplied microphone and then start the measurement. It will generate a series of loud successive sweeps from very low to somewhere around 200 Hz and after a few minutes you are all set (you can increase the listening area with multiple measurements of you want to). This is done with just the subwoofer - you leave the amplifier and the main speakers off. After that you turn on the amplifier and you can start adjusting the subwoofer level and crossover frequency. These you do manually and either by ear, or by measuring in REW, just like you would do without an Antimode.
There are two current models of the Antimode 8033, the Antimode Cinema and the AntimodeS-II. For most people the cheaper Cinema model is perfectly fine (forget its inappropriate name), also for use with multiple (mono) subs. Do read the manual first before you buy, to see if you really need the more expensive model (I didn’t). In my case I had to connect it at speaker level at the amplifier side and at line level at the sub side, using an attenuating cable from amplifer to Antimode.
The whole process will not take more than say half an hour, is absolutely dead easy, and only requires that you read the manual carefully.

I leave my Antimode Cinema on all the time. It will turn on automatically if you plug it in. Power consumption is really minimal.
I don't believe REL are the only manufacturer of good subwoofers for music, however good they are.