The right answer isn't obvious.
While Vodafone's 5% yield is attractive, the payout only rose by 2% last year. Another concern is that this year's forecast payout of 11.6p is only 50% covered by expected earnings.
The special dividends that shareholders used to enjoy when Vodafone owned a stake in Verizon Wireless are a distant memory. Vodafone hasn't yet been able to replace the profits Verizon used to provide.
In my view, Vodafone's dividend is likely to remain pretty much flat for at least another couple of years. However, the firm's massive £19bn programme of capital expenditure is now nearing completion. Trading results from depressed southern European markets also appear to be improving.
A combination of rising sales and falling expenditure could give Vodafone's profits a significant boost, putting the firm's dividend on a much firmer footing. It's notable that the City has been happy to trust Vodafone's management to deliver on its promise to maintain the dividend during this sustained period of investment.
In contrast to many of Vodafone's FTSE 100 peers, broker forecasts do not suggest a dividend cut for this year or next year.
What about BT?
The situation at BT is rather different. BT took on £5bn of extra debt last year as a result of its acquisition of mobile operator EE. This doubled the group's net debt to £9.8bn. BT also plans to spend a further £6bn over the next three years, upgrading its UK fibre network and 4G coverage to provide a more universal service.
All of this will have to be paid for. Although BT generated an impressive £3bn of free cash flow last year, the firm has a lot of calls on its cash.
The group's troublesome £5.2bn pension deficit required a £900m deficit reduction payment last year. Last year's dividend will have cost £1.4bn. Last year's interest payment of £558m is likely to be much higher this year, given the group's extra debt.
While BT has committed to increase the dividend by at least 10% for the next two years, I think this payout might soon start to look less affordable.
Despite my concerns, BT is a very profitable business. The firm's operating margin has averaged about 16% over the last five years. This compares very favourably with Vodafone, which reported an operating margin of just 3.4% last year. The only thing to remember is that Vodafone's margin used to be much higher. In 2012, it peaked at 14.5%.
If Vodafone's investment programme helps the firm return to historic levels of profitability, the group's earnings could rise significantly. That can't be said of BT, where profit margins are already at record highs.
In reality, I don't think there's any way of knowing which share will return more to shareholders over the next few years. That's why I'm going to hold onto my Vodafone shares.
In the face of stock market uncertainty, it's often best to do nothing.
Roland Head has no position in any shares mentioned. The Motley Fool UK has no position in any of the shares mentioned. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.