Plutonium bombs have the advantage that Pu-239 is available because it is made in the waste product of nuclear reactors and can easily be chemically reprocessed. However, the plutonium bomb design and construction is extremely difficult and precise. Plutonium is often contaminated by Pu-240, which is very reactive and decays before the chain reaction goes to completion. So to prevent this from happening, plutonium bombs use implosion. Explosives are detonated on all sides of a mass of Pu to compress it into a small "blob" where the three neutrons emitted can hit other Pu-239 atoms quickly and continue the chain reaction. But the explosions must be entirely balanced and uniform to implode the Pu properly and successfully detonate a Plutonium bomb.
Not to mention the fact that U-234 is 0.0055% of natural uranium. This means take 1000 kg of pure uranium, and only 55 grams of it is U-234. You're better off making a bomb out of the U235 you have. Plus it has a horrible fission cross section http://wwwndc.tokai-sc.jaea.go.jp/cgi-bin/Tab80WWW.cgi?/data/JENDL/JENDL-3.3prc/intern/U234.intern [Broken].