Whilst I agree that it's daft to put the two shows up against one another, as a fan of both shows I still manage to watch both - I usually watch X-Factor and record Strictly (partially because I can then fast forward through Bruce, but also because I'm more likely to watch bits of Strictly back again).
The only thing I think they need to do is switch the Andrew Lloyd Webber show and So You Think You Can Dance in the schedules (although I think So You Think.... might be later than normal this year for reasons other than So You Think... although I could be wrong. If they do that here's the schedule:
End of Winter / Spring
BBC - ALW show (singing)
ITV - Dancing On Ice (dancing/performance based)
Late Spring / Early Summer
BBC - So You Think (dancing/performance)
ITV - BGT (variety, some performance, a fair bit of music/singing)
Autumn / Winter (where the highest ratings are so put on the big hitters)
BBC - Strictly (dancing/performance)
ITV - X-Factor (singing)
The reason I swapped So You Think... and ALW rather than Dancing on Ice and BGT is because by swapping the BBC shows we avoid having Simon Cowell on screen weekly from end-August until sometime in March; and because this way So You Think (arguably the show that needs the biggest publicity push out of all the ones listed) could have Dr Who as a lead-in instead of Total Wipeout or Hole in The Wall - after all, if you've seen one episode of either of those you've seen them all.
By swapping the shows we also get a balance of musical and performance shows up against each other at each time of the year, which means (in my opinion) a better choice for the viewer than having 2 similar shows on at similar times of the year.