3-4 dB dip at crossover region: what should I listen for to hear it?

Any speaker or combinations of them will have their own peaks & dips, it's own response to an input....it's 'voicing' can either be a 'love it' or eq it to 'make it sound OK' in ones' space....

...and the graphs will reflect hat.....not that the unit will sound 'better' or 'worse', it just shifts the perception to the listener v. the means of measuring of such.

I've messed about with various 'n sundry....and you can only 'tweak' so much before the basic 'characteristics' of a speaker in a very subtle fashion until it turns to muck....mho, of course....

@erik_squires, thanks, that makes sense.

Funny you mention Altecs -- I don’t have much experience with horn speakers other than some old Altec Lancings my friend runs with a pair of MC30s. The 4349s remind me of those speakers more than any others I’ve heard. My friend’s system was my first exposure to hifi beyond the Bose 301s and Sony Receiver I had at the time, so its sound is engrained in my memory.

@james633, yeah, I think I'll start a thread for the 4367s and 4349s -- I'd  be interested in reading about both models.

What's an example of a currently produced speaker in the 4349's price range (give or take) that has similar dynamics and sound quality but measure better? 

OP:  I dont' know about better, but I heard the Klipsch Heresy's with a Rogue integrated and really liked them. 

A couple of comments:

Frequency response is measured with continuous signal at 1 watt of input.  This does not take into account what happens when things really get moving and music is played through them.   The linearity of a steady state output at 1 watt may be quite different  from a transient of a few microseconds at, say, 80 watts. Music played at a "normal" listening levels may exhibit little perceived (or measurable) differences in frequency response.  

At the crossover point, 2 drivers (typically) are playing the same signal at, or about, the same volume level.  These drivers may be vastly different in design: materials, cone area, motor structure, or technology thus having varied characteristics in resolution, dispersion, speed, dynamic headroom, etc.  The "weirdness" that can occur to dynamic signals in the narrow range of the crossover points can't be predicted with standard frequency response measurements.

You've got to give them a listen.  In your room.