I have been browsing the forums for quite some time now as I'm looking to invest in an Espresso machine. I've read some good words about:

Izzo Alex Duetto II and
Vibiemme Domobar Super Espresso Machine.

A barista friend of mine, suggested Nuova Simonelli Musica.

Can you please compare these 3 machines and give me your opinion?

As high-end, prosumer DBs, the VBM and Izzo are very similar to one another. The Musica, as an HX, is in another category altogether.

If you're serious about an HX, you might consider making the leap to one f the $3K true professionals like the Elektra T1 and La Cimbali Casa.

BDL

The Musica, as an HX, is in another category altogether

Meaning it's actually considered better?

The thing is that I can get a brand new Musica for 1400 euros (a friend of a friend got one for a small coffee shop that he wanted to open, but by the time it arrived he had already found a partner and went for a bigger investment; so he is selling it to me brand new, not even opened box for 1400 euros).

Do you consider it a good investment? Can I get something better for that amount of money?

First, my apologies for misreading your OP. The VBM Domobar is an HX just like the Musica. It's the Double Domobar which is VBM's double boiler.

As a system within a high quality espresso machine, HX is neither better nor worse than DB -- just slightly different. And for that matter, the importance of the differences is usually exaggerated.

BDL

The musica is a decent machine but what is the price difference from that and the Vibiemme for you? I have the Vibiemme and its a superior HX machine in terms of quality and temp stability. If the musica is significantly cheaper then i would consider it. If its the same price I'd get the Vibiemme

What he's saying is that the Elektra and the Cimbali are better.

And, that for more experienced baristas there would be no real advantage in a DB vis a vis a HX ...

There should be no significant differences in the results you may obtain with any one of these, it's more something about nuances and personal preferences.

The Musica is, for what I've heard, upgraded, completed and much better looking, but still basically it's an Oscar.
That is not bad as it uses some of Nuova Simonelli's much appreciated technical professional solutions, however build in a more economical (admirers would say rational) "way" than the other two.

The price difference between Vibiemme and Musica is 150 euros for me (Musica is 150 euros = $200 cheaper).

The price difference between Izzo and Musica is 260 euros (Musica is 260 euros = $350 cheaper).

Izzo and Vibiemme come with an extended 2 year warranty, a $100 gift certificate and a $75 gift pack though.

That is not a significant difference, considering that it's a medium to long term purchase.
Without having tested any one of these, just for the rotary pump, looks and further specifications I (just an impulse personal choice) would go with the Izzo.

IZZO hands down!

Since bmb mentioned it izzo seems to be the only one that has a rotary pump among the 3. Will the pump type have any significant impact on the noise that machine makes and the quality of the espresso produced? I've read many contradicting opinions on the subject.