My USA Dimension Deluxe HH 4 was an amazing sounding and playing bass by my standards. I found that all freqs were well represented and despite that there is no single coil option, the signal maintained great clarity and note definition, which is a must-have for me, and something I rarely get from humbucker-only pickups. The EQ seemed perfectly voiced and was very powerful. I couldn't find an unpleasant tone anywhere.
As others have mentioned the Dimension puts out a lot of hi-mids, but it's not "trapped" in that space, easily EQ'd to virtually any sonic space. But....I suspect this may only be the case with the HH models. The extra forward pickup may make all the difference. I've found this to also be the difference between a G&L L-1500 and an L-2000. The L-1500 simply doesn't have the heft of the L-2000, so those looking for strong lows and low-mids might not gel with an L-1500. I haven't played a Dimension H....I might hate it too, dunno.
Back to the "hi-mids" aspect...I'm not getting why folks think strong hi-mids are the reason they're getting lost in a mix. For me, those freqs equate to presence. Isn't that, along with cutting lows, the path to being heard in a busy mix? It always has been for me. I'm reminded of descriptions by some Sadowsky players who've described their Sads as sounding a bit middy and harsh solo'd, but absolutely magical in a live mix. I haven't owned a Sadowsky, but I understand the principle behind why some owners feel that way. My Dimension shined best while playing with others.