Bhrigu Express: बलिया की आन बान और शान , भृगु एक्सप्रेस है तुम्हारा नाम। हर रविवार तुमसे मिलना है मेरा काम। - Shanzil Kabir

I am speaking only for MAS - TVC end to end pax.
I agree people will prefer trains over their counterpart taking much time/travel less distance or based on the timings. Classic example is Charminar over Chennai-Kacheguda Express.
Reason: The route taken by Kaceguda is not safe compared to Charminar. In the case of Anatapuri i dont see any disparity with respect to routes travelled.
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to below reasons. I am saying it by looking at the future prospects and not at today's sense.
1. Both are ICF Rakes with same class of travel availability. SL, 3A, 2A & 1A.
2 Both will be SF
3. Anatapuri will be augumented with more coaches.
4. Punctuality wise similar. TVC SF mail don't reach Chennai on time for most of the occasions. Reach on time or within 30 mins delay range.
Trains in MAS - CBE sector on an average takes 7 Hrs 30 Mins - 45 Mins for normal SF trains which don't have final destination as CBE. Like wise Anatapuri could take 7 Hrs 45 Mins to 8 Hrs to MDU.
TEN - 10 Hrs 30 Mins. Currently SF trains take 2 Hrs 30 Mins from MDU to TEN.
NCJ: 11 Hrs 30 Mins.
TVC: 13 Hrs to 13 Hrs 30 Mins. Max 14 Hours. Even then 2+ Hrs difference between TVC SF Mail which takes 16 Hrs 30 Mins.
No loco change will be required en route. One loco reversal will be needed at NCJ.
Currently KK takes 12 Hrs 40 Mins to NCJ.
Note: I am speaking only for TVC pax preference for train and not on TVC Mail as an whole entity.
If Anatapuri starts at 6/6:30 and reaches TVC around 8 AM it will be the perfect over nighter train for MAS - TVC.