Ti and Ta indeed have nothing to see, except that they are both biocompatible anc corrosion-resistant, like gold and platinum. But the latter two metals are far too ductile, so they can't be used as implant. Ti, on the contrary, is excellent for that purpose, because of it exceptional specific resistance (hence its use in aerospace applications). But Ti may be too elastic for some medical applications requiring a tougher material, hence the use of Ta. And because of its high density and high cost, Ta will indeed never be used in aerospace applications.

Alain

There are many considerations for each use and many different uses in each field.

One example: the density of Ta is almost 4 times higher than Ti, which could explain Ta's scarcity in aerospace applications.

The question is much more complex and I don't recall seeing these two metals 'compete' for the same function. Ta is quite expensive compared to Ti and its advantages include high thermal stability and chemical stability. Ti is considerably cheaper, and a key advantage of it is high specific strength (stength/weight ratio).

There are countless additional features and considerations.

Ti and Ta indeed have nothing to see, except that they are both biocompatible anc corrosion-resistant, like gold and platinum. But the latter two metals are far too ductile, so they can't be used as implant. Ti, on the contrary, is excellent for that purpose, because of it exceptional specific resistance (hence its use in aerospace applications). But Ti may be too elastic for some medical applications requiring a tougher material, hence the use of Ta. And because of its high density and high cost, Ta will indeed never be used in aerospace applications.

Alain

I agree that both elements neither compete in the medical nor in the aerospace sector as they are very different in many ways. Due to its high density, it is very unlikely that Ta-base alloys will ever be used in aerospace applications. As the purpose of your question is not really clear to me, you might want to take into account that Ta is often used as alloying element in alloys being applied in both sectors.

Ta is a strong beta stabilizer in Ti but there are other cheaper elements like V or Mo which are used e.g. in landing gear alloys like Ti 5Al 5V 5Mo 3Cr or Ti 15V 3Al 3Cr 3Sn. On the other hand, in fully stabilized beta-Titanium alloys like Ti 35Nb 7Zr 5Ta (planned to be used as implant materials as their Young's modulus is close to that of human bones), Ta is used instead of other (toxic) beta-stabilizers like V.

In aerospace applications you find both Ti and Ta as alloying elements in Co- or Ni-base alloys, stabilizing the gamma’ phase.

Ti, owing to its low density, and good mechanical properties is used in both aerospace and medical applications. In fact Ti alloys such as Ti-6-4 have commercial applications in Knee implants. Tantalum on the other hand, has its own advantages but doesn't compete with Titanium.

Both tantalum and titanium possess excellent corrosion resistance and can be considered biocompatible. Ta is highly refractory and has found several applications in electronics (e.g. capacitors). Being highly malleable and ductile, Ta can be shaped as very thin foil, or as wire of very high tensile strength, which compares favourably to most other metals (including Ti). Ti and its alloys generically possess superior specific fracture toughness (toughness-weight ratio), specific tensile strength, and fatigue strength. They are hence usually preferred as load-bearing orthopaedic implant materials. Lower density and cost also favour their application as structural materials by the aerospatial industry.       

Tantalum is having excellent corrosion resistance and it is biocompatible and these properties are better than that Titanium. As per the density, wise tantalum is very dense than titanium hence it is not suitable to use in the aerospace application.

It is known that the tantalum is having very high young's modulus than that of a normal bone which can cause stress shielding effect in the bone but it can be easily removed by making tantalum as a porous structure which also helps in osseointegration process and formation of a new blood vessel in bone implant. Tantalum also showed the formation of Hydroxyapatite layer when immersed in Simulated body fluid which is a good sign for its use for bioimplants.