I am a firm believer in "both kinds of DX": live and after-the-fact 
capture analysis.
Whenever possible you should use a mix of the old-school and 
new-school methods.
Advantages of live DXing:
* You can use webstream, remote-receiver, and shortwave parallels.
* You can use high-Q tuned antennas rather than broadband.  In two 
situations this is the way to go.  One would be when you have very 
weak signal conditions and not enough space for a broadband antenna 
of sufficient sensitivity.  The other would be when you are in an 
urban situation where any broadband antenna of sufficient gain to 
hear DX is going to present locals at such high levels that the 
receiver will create spurious signals.
* You can use a phasing unit to target the specific "pest" affecting 
the frequency on which you're actively DXing at the time.  It takes 
a very good antenna system (e.g. physically-large array) to deliver 
much better than a 25 dB null in a broadband sense.  But narrow 
bandwidth nulls of better than 40 dB are easily had with a Quantum 
Phaser (or similar) and a pair of different-pick-up antennas (e.g. 
loop vs. whip, loops at right angle), or with two similar-pick-up 
antennas spaced at least 50m / 164 ft. apart.
Advantage of after-the-fact capture analysis (Perseus, Excalibur, etc.)
* During a "hot" opening, a single top-of-hour capture gets you a 
whole medium-wave band worth of ID's.  This would take much more 
time to accomplish with live DX sessions.  Optimum conditions may 
have gone away by the time you're even halfway through the band 
doing it live.
At US/Canada East Coast beach sites around local sunset, two 
top-of-hour captures (+/- 3 min.) can get you an amazing amount of 
choice DX.  Same is true for West Coast around local dawn.  And, if 
it's auroral, admittedly a fairly rare occurrence in recent years, 
you'll be busy all night on tops-of-hour as well as on the 
half-hours for the Venezuelans.
* You can repeatedly replay a given target, trying AM, synchro AM, 
USB, and LSB modes; various IF bandwidths; notch filters et al.  On 
live DXing you have less time to figure out the optimum receiver settings.
Since you typically won't have webstreams and shortwave to assist 
you on after-the-fact analysis of medium wave capture files, use the 
periods BETWEEN the tops-of-hour (:00+/-3) and bottoms-of-hour 
(:30+/-2) captures to do live DX, making sure to avail yourself of 
things that are only feasible when DXing the old-school way.  You 
can still have TotalRecorder (or your other favorite audio recording 
tool) running during the live DX activity since you won't want proof 
of a breathtakingly rare catch passing you by.  What you find out 
during the between-captures live DX will feed into antenna-aiming 
etc. decisions you may want to make before the next capture session.