It helps to separate the two questions. A personal account is about you: your identity, residence, income and tax position. A business account is about the company: its licence, activity, owners, substance and expected transactions. Banks assess them separately, and having one does not guarantee the other. Many founders open a personal account first once their visa is issued, because a local account makes paying rent, utilities and visa fees easier, and the existing relationship can make the business application smoother.
For business accounts, the company's licence must permit the activity it plans to bank, the expected inflows must make sense for its size, and at least one person connected to it is usually expected to be UAE resident. Foreign companies without a UAE licence will find very few Dubai banks willing to open accounts for them, and those that do generally serve large multinational clients.
Currency is rarely the obstacle. UAE banks commonly offer dirham, US dollar, euro and pound accounts, and the dirham's peg to the dollar makes Dubai a practical base for dollar-denominated trade. The obstacles are almost always about who you are, what the money is for and whether the UAE is a natural place for that activity. Answering those three questions clearly and with evidence does most of the work.
It is also worth thinking about the long term. Banks periodically refresh client files, and an account opened with thin documentation may be reviewed and closed later if activity drifts from what was declared. Keeping the bank informed of material changes, such as new products, new countries or a large rise in volume, avoids surprises.